Stock Price Trends

Pitney Bowes Inc (PBI)

Pitney Bowes Inc., a technology company, offers business solutions in the United States and internationally. The company is headquartered in Stamford, Connecticut.

Stock Price Trends

Stock price trends estimated using linear regression.

Key facts

  • The primary trend is increasing.
  • The growth rate of the primary trend is 109.22% per annum.
  • PBI price at the close of November 19, 2024 was $7.76 and was inside the primary price channel.
  • The secondary trend is increasing.
  • The growth rate of the secondary trend is 172.46% per annum.
  • PBI price at the close of November 19, 2024 was inside the secondary price channel.

Linear Regression Model

Model equation:
Yi = α + β × Xi + εi

Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)

Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)

where:

i - observation number
Yi - natural logarithm of PBI price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e


Primary Trend

Start date: August 3, 2023
End date: November 19, 2024

a = -1.6829

b = 0.0020

s = 0.0961

Annual growth rate:

Exp(365 × b) – 1
= Exp(365 × 0.0020) – 1
= 109.22%

Price channel spread:

Exp(4 × s) – 1
= Exp(4 × 0.0961) – 1
= 46.86%

August 3, 2023 calculations

Top border of price channel:

Exp(Y930)
= Exp(a + b × X930 + 2 × s)
= Exp(a + b × 1,352 + 2 × s)
= Exp(-1.6829 + 0.0020 × 1,352 + 2 × 0.0961)
= Exp(1.2436)
= $3.47

Bottom border of price channel:

Exp(Y930)
= Exp(a + b × X930 – 2 × s)
= Exp(a + b × 1,352 – 2 × s)
= Exp(-1.6829 + 0.0020 × 1,352 – 2 × 0.0961)
= Exp(0.8593)
= $2.36

November 19, 2024 calculations

Top border of price channel:

Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(-1.6829 + 0.0020 × 1,826 + 2 × 0.0961)
= Exp(2.2022)
= $9.04

Bottom border of price channel:

Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(-1.6829 + 0.0020 × 1,826 – 2 × 0.0961)
= Exp(1.8179)
= $6.16

Description

  • The primary trend is increasing.
  • The growth rate of the primary trend is 109.22% per annum.
  • PBI price at the close of November 19, 2024 was $7.76 and was inside the primary price channel.

Secondary Trend

Start date: February 5, 2024
End date: November 19, 2024

a = -2.9214

b = 0.0027

s = 0.0807

Annual growth rate:

Exp(365 × b) – 1
= Exp(365 × 0.0027) – 1
= 172.46%

Price channel spread:

Exp(4 × s) – 1
= Exp(4 × 0.0807) – 1
= 38.11%

February 5, 2024 calculations

Top border of price channel:

Exp(Y1,057)
= Exp(a + b × X1,057 + 2 × s)
= Exp(a + b × 1,538 + 2 × s)
= Exp(-2.9214 + 0.0027 × 1,538 + 2 × 0.0807)
= Exp(1.4635)
= $4.32

Bottom border of price channel:

Exp(Y1,057)
= Exp(a + b × X1,057 – 2 × s)
= Exp(a + b × 1,538 – 2 × s)
= Exp(-2.9214 + 0.0027 × 1,538 – 2 × 0.0807)
= Exp(1.1407)
= $3.13

November 19, 2024 calculations

Top border of price channel:

Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(-2.9214 + 0.0027 × 1,826 + 2 × 0.0807)
= Exp(2.2544)
= $9.53

Bottom border of price channel:

Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(-2.9214 + 0.0027 × 1,826 – 2 × 0.0807)
= Exp(1.9316)
= $6.90

Description

  • The secondary trend is increasing.
  • The growth rate of the secondary trend is 172.46% per annum.
  • PBI price at the close of November 19, 2024 was inside the secondary price channel.