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 65.93% per annum.
  • PBI price at the close of July 26, 2024 was $6.74 and was higher than the top border of the primary price channel by $0.12 (1.79%).
  • The secondary trend is increasing.
  • The growth rate of the secondary trend is 264.52% per annum.
  • PBI price at the close of July 26, 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: May 1, 2023
End date: July 26, 2024

a = -0.8492

b = 0.0014

s = 0.1044

Annual growth rate:

Exp(365 × b) – 1
= Exp(365 × 0.0014) – 1
= 65.93%

Price channel spread:

Exp(4 × s) – 1
= Exp(4 × 0.1044) – 1
= 51.82%

May 1, 2023 calculations

Top border of price channel:

Exp(Y946)
= Exp(a + b × X946 + 2 × s)
= Exp(a + b × 1,372 + 2 × s)
= Exp(-0.8492 + 0.0014 × 1,372 + 2 × 0.1044)
= Exp(1.2632)
= $3.54

Bottom border of price channel:

Exp(Y946)
= Exp(a + b × X946 – 2 × s)
= Exp(a + b × 1,372 – 2 × s)
= Exp(-0.8492 + 0.0014 × 1,372 – 2 × 0.1044)
= Exp(0.8456)
= $2.33

July 26, 2024 calculations

Top border of price channel:

Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(-0.8492 + 0.0014 × 1,824 + 2 × 0.1044)
= Exp(1.8903)
= $6.62

Bottom border of price channel:

Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(-0.8492 + 0.0014 × 1,824 – 2 × 0.1044)
= Exp(1.4727)
= $4.36

Description

  • The primary trend is increasing.
  • The growth rate of the primary trend is 65.93% per annum.
  • PBI price at the close of July 26, 2024 was $6.74 and was higher than the top border of the primary price channel by $0.12 (1.79%).

Secondary Trend

Start date: February 20, 2024
End date: July 26, 2024

a = -4.6137

b = 0.0035

s = 0.0819

Annual growth rate:

Exp(365 × b) – 1
= Exp(365 × 0.0035) – 1
= 264.52%

Price channel spread:

Exp(4 × s) – 1
= Exp(4 × 0.0819) – 1
= 38.75%

February 20, 2024 calculations

Top border of price channel:

Exp(Y1,148)
= Exp(a + b × X1,148 + 2 × s)
= Exp(a + b × 1,667 + 2 × s)
= Exp(-4.6137 + 0.0035 × 1,667 + 2 × 0.0819)
= Exp(1.4571)
= $4.29

Bottom border of price channel:

Exp(Y1,148)
= Exp(a + b × X1,148 – 2 × s)
= Exp(a + b × 1,667 – 2 × s)
= Exp(-4.6137 + 0.0035 × 1,667 – 2 × 0.0819)
= Exp(1.1296)
= $3.09

July 26, 2024 calculations

Top border of price channel:

Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(-4.6137 + 0.0035 × 1,824 + 2 × 0.0819)
= Exp(2.0135)
= $7.49

Bottom border of price channel:

Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(-4.6137 + 0.0035 × 1,824 – 2 × 0.0819)
= Exp(1.6860)
= $5.40

Description

  • The secondary trend is increasing.
  • The growth rate of the secondary trend is 264.52% per annum.
  • PBI price at the close of July 26, 2024 was inside the secondary price channel.